Velocity & acceleration

I heard it would be possible to have zero velocity & non zero acceleration (I know the opposite situation where there is velocity (constant), but zero acceleration). Could anyone please give me a clue on this?

The prior post documents the only practical type case I can think of at the moment. A similar situation without velocity reversal could be a boat accelerating against a river current...as observed from shore.

An abstract situation might be at the moment when a distant observer sees a spaceship accelerating towards him and when the velocity reaches the observed cosmic expansion speed at the location of the spaceship, the observer would measure zero velocity...

How about an accelerating plane being overtaken by another higher fixed speed plane: at the moment the speeds are equal, velocity would be zero.

However, here's your chance to prove yourself: If the acceleration is 0 at the top of the ball's trajectory and 9.8 m/s2 on the way back down, at what point in time, t, does the acceleration become nonzero and what is the acceleration at that point?

where [itex]v_0[/itex] is the initial velocity, and we let this to be positive since it was tossed upwards.

Now PLOT that as a function of t. You'll see that as gt grows in value, v will become smaller, until at some point, [itex]-gt + v_0[/itex] is zero! But look at how this was derived. It was derived for a constant acceleration of -g!! Throughout the whole motion, the acceleration is a constant!

The prior post documents the only practical type case I can think of at the moment. A similar situation without velocity reversal could be a boat accelerating against a river current...as observed from shore.

Try the oscillating motion of a mass in a simple mass-spring harmonic oscillator. At the maximum extension, the mass temporarily has a zero velocity, but the acceleration is maximum.

I heard it would be possible to have zero velocity & non zero acceleration (I know the opposite situation where there is velocity (constant), but zero acceleration). Could anyone please give me a clue on this?

OK, you can have an instantaneous velocity of 0, but at that point isn't your instantaneous acceleration also 0?

The problem here is that you have a fundamental misunderstanding of what acceleration means in relation to velocity. Consider a curve of velocity vs. time. At some time, t, the instantaneous velocity is zero. The acceleration is the slope of the velocity curve at time t. You are confusing a value on a curve with its slope.